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University of Pennsylvania ScholarlyCommons Summer Program for Undergraduate Research (SPUR) Wharton Undergraduate Research 8-24-2017 Exploring the Impacts of Salary Allocation on Team Performance Jimmy Gao University of Pennsylvania Follow this and additional works at: https://repository.upenn.edu/spur Part of the Applied Statistics Commons, Business Analytics Commons, Sports Management Commons, Sports Studies Commons, and the Statistical Models Commons Recommended Citation Gao, J. (2017). "Exploring the Impacts of Salary Allocation on Team Performance," Summer Program for Undergraduate Research (SPUR). Available at https://repository.upenn.edu/spur/23 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/spur/23 For more information, please contact [email protected]. Exploring the Impacts of Salary Allocation on Team Performance Abstract Study of salary has been an increasingly important area in professional sports literature. In particular, salary allocation can be a significant factor of team performance in NBA, given credit to the wisdom of team managers. This paper seeks to extend the scope of existing research on basketball by investigating on how salary allocation affected team performance and exploring other factors that lead to team success. Our findings indicate a moderate correlation between salary allocation and team performance, while average Player Efficiency Rating is a more crucial factor of team performance in comparison. Keywords Basketball, Salary Allocation, Player Efficiency Rating (PER), Superstar Effect, Golden State Warriors Disciplines Applied Statistics | Business Analytics | Sports Management | Sports Studies | Statistical Models This working paper is available at ScholarlyCommons: https://repository.upenn.edu/spur/23 Exploring the Impact of Salary Allocation on NBA Team Performance Acknowledgement I would like to thank Dr. Schurmans for accepting me into the SPUR program and encouraging me to do research. I’d like to thank Professor Veeraraghavan for serving as my research advisor and providing guidance throughout my research experience. Abstract Study of salary has been an increasingly important area in professional sports literature. In particular, salary allocation can be a significant factor of team performance in NBA, given credit to the wisdom of team managers. This paper seeks to extend the scope of existing research on basketball by investigating on how salary allocation affected team performance and exploring other factors that lead to team success. Our findings indicate a moderate correlation between salary allocation and team performance, while average Player Efficiency Rating is a more crucial factor of team performance in comparison. Keywords salary allocation, Player Efficiency Rating (PER), Superstar Effect, Golden State Warriors Disciplines Sports | Basketball | National Basketball Association (NBA) |Salary and Team Performance Analysis 1. Introduction There has been an increasing research interest in the relations between salary allocation and team success in professional sports over the years. A number of researchers have investigated on whether the amount of salary impacted the team success, measured by different metrics ranging from team revenue to winning percentage. Research has indicated a positive correlation between the team payroll and team success. These research studies encompass multiple sports such as basketball, football, baseball and ice hockey, with a focus on the four major professional leagues in the United States and Canada. Over the past several years, the salary cap in National Basketball Association (NBA) has been increasing drastically, with a further projected increase after the league signed a gigantic nine-year, $24-billion TV-deal this year.1 Evident from the changes from the 2015-2016 season to the 2016- 2017 season, the salary cap rose from $70 million to $94 million by a whopping $24 million while the luxury tax limit also increased from $85 million to $113 million by $28 million, an even larger amount at.2 This trend, known as the ‘Superstar Effect’, creates further opportunities for teams to sign multiple superstars to compete for championships: the best example comes from the former Oklahoma City Thunder superstar small forward Kevin Durant, who was able to sign with the Golden State Warriors in the 2016 off-season because of the increase in the salary cap and Warriors superstar Stephen Curry’s surprisingly low four-year, $44-million contract that took his previous ankle injuries into consideration.3 Later, with four NBA All-Stars in their starting lineup, the 2017 Warriors were considered as the most talented team in the NBA history and was described as a 1 Prada, 2014 2 Zillgitt, 2017 3 Badenhausen, 2017 ‘juggernaut’ by Forbes Magazine contributor Vincent Crank,4 crowning the Larry O’Brien trophy after finishing the playoffs with a historic 16-1 run in 2017. Seeing the significance of salary in professional basketball leagues on team success, this paper will take a statistical approach to investigate on the relationship between the allocation of salary in an NBA team and team success, measured mainly by the winning percentage out of 82 games during the regular season. While advancing to the playoffs and accomplishing a championship are also good indicators of team performance, we choose the team winning percentage during the regular season because team performance is more consistent during this time span compared with post-season playoffs where winning is highly affected by external factors such as home court advantage. According to recent basketball research conducted by Larry Coon in 2017, the correlation between team payroll and regular season wins is very strong. For the 2010-11 NBA season, the correlation coefficient1 between team payroll and regular season wins was 0.535 ------ high enough to conclude that teams with deep roster have been able to achieve success simply by spending more money on talent, at least to some extent. Although the recent correlation coefficient for the 2016~2017 season declined to 0.353, this statistical result still demonstrated a moderate correlation between the two. This paper takes one step further to investigate on the impacts of the salary on NBA teams, specifically on how the allocation of the salary affected the performance of these teams during the regular season across different years. Furthermore, this paper goes beyond salary distribution to investigate on other key factors that affect team success on the basketball. Section 2 of the paper explores how data is cleaned and organized. Section 3 synthesizes the analysis of Section 2 and constructs a model on the team performance by using the winning percentage of the team during the regular season as a key metric. 4 Frank, 2017 5 Coon, 2017 2. Data and Methodology In this section, we discuss how the data about the team performance and salary of players is scraped from the Internet and cleaned. We then process data to explore the correlation between the salary distribution and team performance. Through several stages of analysis, we choose to investigate additional factors that affect the team performance along with the salary distribution. 2.1 Data Scraping and Cleaning Since the winning percentage of NBA teams during the regular season is the most direct measure of team performance, we extracted the data on the number of wins for all 30 NBA teams during five regular seasons from 2012 to 2017 due to a steady increase in salary cap from 2011 and omitted the 2011-2012 season because it was shortened to 66 games. Because all teams play 82 games during the regular season, the winning percentage can be calculated by the formula: No. of Wins in a Season Team Winning Percentage = 82 In order to measure the salary distribution of NBA teams, we have to first get the data about the salary of every single player for all 30 NBA teams from 2012 to 2017. We choose to use data from a website called Basketball Reference because it takes into account the movement of players during trades and signings of free agents in the middle of the season. After scraping the data with R, we have 150 columns of data representing the salary breakdown of 30 teams during the past five regular seasons. To measure the salary distribution in a team, we use three different metrics: standard deviation, Gini Coefficient and Robin Hood Coefficient. The standard deviation measures how much the salary of each player in the team deviates from the mean. Gini Coefficient and Robin Hood Coefficient, in comparison with standard deviation, are more general measurements of dispersion because they are invariant of scale and are bounded by [0, 1]. While these two metrics are commonly used to measure the income inequality of countries at a macroeconomic level, they can also be used in the measurement of wealth inequality6 such as salary distribution in this context. However, these two coefficients also possess certain limitations: the two coefficients will have a downward bias on the measurement of salary distribution because the data size for each team during a season is very small, ranging from 13 to 28 players. This leads to an underestimation of salary inequality in a team, thus affecting the correlation between salary distribution and team winning percentage. 2.2 Finding Correlation After calculating the Gini Coefficient and Robin Hood Coefficient of all 30 NBA teams across the past five seasons, we run a correlation test between the team winning percentage and these three metrics of salary distribution including the standard deviation of salary with Python. Before doing so, we first standardize the salary distribution and team winning percentage data with the following formula: � − E(�) Standardized � = σ Measure of Salary Distribution Correlation with Team Winning Percentage Standard Deviation 0.309 Gini Coefficient 0.035 Robin Hood Coefficient 0.100 Table 1: Correlation with Team Winning Percentage for Different Measures of Salary Distribution According to Table 1, we find the highest correlation with team winning percentage in the standard deviation of salary at 0.309, which is also demonstrated in Figure 1 below when a regression is run against these variables.
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